Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5

Average Error: 0.5 → 0.5

Time: 36.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]

↓

\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\left(3 \cdot \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right) + \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right)\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

C

double f(double x, double y) {
        double r424577 = 2.0;
        double r424578 = sqrt(r424577);
        double r424579 = x;
        double r424580 = sin(r424579);
        double r424581 = y;
        double r424582 = sin(r424581);
        double r424583 = 16.0;
        double r424584 = r424582 / r424583;
        double r424585 = r424580 - r424584;
        double r424586 = r424578 * r424585;
        double r424587 = r424580 / r424583;
        double r424588 = r424582 - r424587;
        double r424589 = r424586 * r424588;
        double r424590 = cos(r424579);
        double r424591 = cos(r424581);
        double r424592 = r424590 - r424591;
        double r424593 = r424589 * r424592;
        double r424594 = r424577 + r424593;
        double r424595 = 3.0;
        double r424596 = 1.0;
        double r424597 = 5.0;
        double r424598 = sqrt(r424597);
        double r424599 = r424598 - r424596;
        double r424600 = r424599 / r424577;
        double r424601 = r424600 * r424590;
        double r424602 = r424596 + r424601;
        double r424603 = r424595 - r424598;
        double r424604 = r424603 / r424577;
        double r424605 = r424604 * r424591;
        double r424606 = r424602 + r424605;
        double r424607 = r424595 * r424606;
        double r424608 = r424594 / r424607;
        return r424608;
}

↓

double f(double x, double y) {
        double r424609 = 2.0;
        double r424610 = sqrt(r424609);
        double r424611 = x;
        double r424612 = sin(r424611);
        double r424613 = y;
        double r424614 = sin(r424613);
        double r424615 = 16.0;
        double r424616 = r424614 / r424615;
        double r424617 = r424612 - r424616;
        double r424618 = r424610 * r424617;
        double r424619 = r424612 / r424615;
        double r424620 = r424614 - r424619;
        double r424621 = r424618 * r424620;
        double r424622 = cos(r424611);
        double r424623 = cos(r424613);
        double r424624 = r424622 - r424623;
        double r424625 = r424621 * r424624;
        double r424626 = r424609 + r424625;
        double r424627 = 3.0;
        double r424628 = r424627 * r424627;
        double r424629 = 5.0;
        double r424630 = r424628 - r424629;
        double r424631 = sqrt(r424629);
        double r424632 = r424627 + r424631;
        double r424633 = r424630 / r424632;
        double r424634 = r424633 / r424609;
        double r424635 = r424634 * r424623;
        double r424636 = 1.0;
        double r424637 = r424631 - r424636;
        double r424638 = r424637 / r424609;
        double r424639 = r424638 * r424622;
        double r424640 = r424636 + r424639;
        double r424641 = r424635 - r424640;
        double r424642 = r424635 * r424641;
        double r424643 = r424640 * r424640;
        double r424644 = r424642 + r424643;
        double r424645 = r424627 * r424644;
        double r424646 = r424640 + r424635;
        double r424647 = r424645 * r424646;
        double r424648 = r424626 / r424647;
        double r424649 = r424633 * r424633;
        double r424650 = 2.0;
        double r424651 = pow(r424623, r424650);
        double r424652 = r424649 * r424651;
        double r424653 = r424633 * r424623;
        double r424654 = r424640 * r424653;
        double r424655 = r424609 * r424654;
        double r424656 = r424652 - r424655;
        double r424657 = r424609 * r424656;
        double r424658 = 3.0;
        double r424659 = pow(r424609, r424658);
        double r424660 = r424657 / r424659;
        double r424661 = r424643 + r424660;
        double r424662 = r424648 * r424661;
        return r424662;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.5

   \[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
2. Using strategy rm

3. Applied flip-- 0.5

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\color{blue}{\frac{3 \cdot 3 - \sqrt{5} \cdot \sqrt{5}}{3 + \sqrt{5}}}}{2} \cdot \cos y\right)}\]

4. Simplified 0.5

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{\color{blue}{3 \cdot 3 - 5}}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
5. Using strategy rm

6. Applied flip3-+ 0.6

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \color{blue}{\frac{{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}}{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)}}}\]

7. Applied associate-*r/ 0.6

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\color{blue}{\frac{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)}{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)}}}\]

8. Applied associate-/r/ 0.6

   \[\leadsto \color{blue}{\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)\right)}\]
9. Using strategy rm

10. Applied associate-*l/ 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \color{blue}{\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y}{2}}\right)\right)\]

11. Applied associate-*r/ 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \color{blue}{\frac{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2}}\right)\right)\]

12. Applied associate-*l/ 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \color{blue}{\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y}{2}} - \frac{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2}\right)\right)\]

13. Applied associate-*l/ 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\color{blue}{\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y}{2}} \cdot \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y}{2} - \frac{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2}\right)\right)\]

14. Applied frac-times 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\color{blue}{\frac{\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2 \cdot 2}} - \frac{\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)}{2}\right)\right)\]

15. Applied frac-sub 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \color{blue}{\frac{\left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right) \cdot 2 - \left(2 \cdot 2\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)}{\left(2 \cdot 2\right) \cdot 2}}\right)\]

16. Simplified 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\color{blue}{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}}{\left(2 \cdot 2\right) \cdot 2}\right)\]

17. Simplified 0.6

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left({\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)}^{3} + {\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}^{3}\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{\color{blue}{{2}^{3}}}\right)\]
18. Using strategy rm

19. Applied sum-cubes 0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \color{blue}{\left(\left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)}} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

20. Applied associate-*r* 0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\color{blue}{\left(3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\right)\right)\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

21. Simplified 0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\color{blue}{\left(3 \cdot \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right) + \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right)\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

22. Final simplification 0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\left(3 \cdot \left(\left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot \left(\frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y - \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right) + \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right)\right)\right) \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)} \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{2 \cdot \left(\left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \frac{3 \cdot 3 - 5}{3 + \sqrt{5}}\right) \cdot {\left(\cos y\right)}^{2} - 2 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) \cdot \left(\frac{3 \cdot 3 - 5}{3 + \sqrt{5}} \cdot \cos y\right)\right)\right)}{{2}^{3}}\right)\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  :precision binary64
  (/ (+ 2 (* (* (* (sqrt 2) (- (sin x) (/ (sin y) 16))) (- (sin y) (/ (sin x) 16))) (- (cos x) (cos y)))) (* 3 (+ (+ 1 (* (/ (- (sqrt 5) 1) 2) (cos x))) (* (/ (- 3 (sqrt 5)) 2) (cos y))))))